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Rigid Bodies

  • Nicholas M. J. WoodhouseEmail author
Chapter
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Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Abstract

The motion of a rigid body at any instant is determined by the six components of two vectors, the angular velocity ω and the velocity u of a chosen point O of the body. There are therefore six degrees of freedom and we should be able to describe the evolution by introducing six generalized coordinates: three for position and three for orientation.

The position coordinates are straightforward because we can use the three Cartesian coordinates of O in some inertial frame. The components of u are then the corresponding generalized velocities. As we saw in Section 1.9, it is a more complicated problem to find convenient coordinates to describe the rotational degrees of freedom. It is, in fact, impossible to find three generalized coordinates for which the three components of ω are the corresponding generalized velocities. Whatever angular coordinates are used, the task of expressing ω in terms of their time derivatives is always a source of complication.

Keywords

Angular Momentum Angular Velocity Rigid Body Principal Axis Rest Frame 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2009

Authors and Affiliations

  1. 1.Mathematical Institute University of OxfordOxfordUnited Kingdom

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